One of the earliest thought experiments originated with the physicist and astronomer Galileo. In order to refute Aristotle’s claim that the speed of a falling object is dictated by its mass, Galileo devised a simple mental example: According to Aristotelian logic, if a light object and a heavy object were tied together and dropped off a tower, then the heavier object would fall faster, and the rope between the two would become taut. This would allow the lighter object to create drag and slow the heavy one down. But Galileo reasoned that once this occurs, the weight of the two objects together should be heavier than the weight of either one by itself, therefore making the system as a whole fall faster. That this is a contradiction proved that Aristotle’s hypothesis was wrong.

What it Means:

One of the most famous stories about Galileo is that he once dropped two metal balls off the Leaning Tower of Pisa to prove that heavier objects do not fall faster than lighter ones. In actuality, this story is probably just a legend; instead, it was this elegant thought experiment that helped prove a very important theory about gravity: no matter their mass, all objects fall at the same rate of speed.

4. Monkeys and Typewriters

Another thought experiment that gets a lot of play in popular culture is what is known as the “infinite monkey theorem.” Also known as the “monkeys and typewriters” experiment, the theorem states that if an infinite number of monkeys were allowed to randomly hit keys on an infinite number of typewriters for an infinite amount of time, then at some point they would “almost surely” produce the complete works of Shakespeare. The monkeys and typewriters idea was popularized in the early 20th century by the French mathematician Emile Borel, but its basic idea—that infinite agents and infinite time will randomly produce anything and everything—dates back to Aristotle.

What it Means:

Simply put, the “monkeys and typewriters” theorem is one of the best ways to illustrate the nature of infinity. The human mind has a difficult time imagining a universe with no end or time that will never cease, and the infinite monkeys help to illustrate the sheer breadth of possibilities these concepts create. The idea that a monkey could write Hamlet by accident seems counterintuitive, but in fact it is mathematically provable when one considers the probabilities. The theorem itself is impossible to recreate in the real world, but that hasn’t stopped some from trying: In 2003, science students at a zoo in the U.K. “tested” the infinite monkey theorem when they put a computer and a keyboard in a primate enclosure. Unfortunately, the monkeys never got around to composing any sonnets. According to researchers, all they managed to produce was five pages consisting almost entirely of the letter “s.”

3. The Chinese Room

The Chinese Room is a famous thought experiment first proposed in the early 1980s by John Searle, a prominent American philosopher. The experiment asks you to imagine that an English speaking man has been placed in a room that is entirely sealed, save for a small mail slot in the chamber door. He has with him a hard copy in English of a computer program that translates the Chinese language. He also has plenty of spare scratch paper, pencils, and file cabinets. Pieces of paper containing Chinese characters are then slipped through the slot in the door. According to Searle, the man should be able to use his book to translate them and then send back his own response in Chinese. Although he doesn’t speak a word of the language, Searle argues that through this process the man in the room could convince anyone on the outside that he was a fluent speaker of Chinese.

What it Means:

Searle conceived the Chinese Room thought experiment in order to refute the argument that computers and other artificial intelligences could actually think and understand. The man in the room does not speak Chinese; he can’t think in the language. But because he has certain tools at his disposal, he would be able convince even a native speaker that he was fluent in it. According to Searle, computers do the same thing. They don’t ever truly understand the information they’re given, but they can run a program, access information, and give a clear impression of human intelligence.

2. Schrodinger’s Cat

Schrödinger’s Cat is a paradox relating to quantum mechanics that was first proposed by the physicist Erwin Schrödinger. It concerns a cat that is sealed inside a box for one hour along with a radioactive element and a vial of deadly poison. There is a 50/50 chance that the radioactive element will decay over the course of the hour. If it does, then a hammer connected to a Geiger counter will trigger, break the vial, release the poison, and kill the cat. Since there is an equal chance that this will or will not happen, Schrödinger argued that before the box is opened the cat is simultaneously both alive and dead.

What it Means:

In short, the point of the experiment is that because there is no one around to witness what had occurred, the cat existed in all of its possible states (in this case either alive or dead) simultaneously. This notion is similar to the old “if a tree falls in the woods and there’s no one there to hear it, does it make a sound?” riddle. Schrödinger originally conceived of his theoretical cat in response to an article that discussed the nature of quantum superpositions, a theory that defines all the possible states in which an object can exist. Schrödinger’s Cat also helped to illustrate just how weird the rules of quantum mechanics really were. The thought experiment is notorious for its complexity, which has encouraged a wide variety of interpretations. One of the most bizarre is the “many worlds” hypothesis, which states that the cat is both alive and dead, and that both cats exist in different universes that will never overlap with one another.

1. Brain in a Vat

There has been no more influential thought experiment than the so-called “brain in a vat” hypothesis, which has permeated everything from cognitive science and philosophy to popular culture. The experiment asks you to imagine a mad scientist has taken your brain from your body and placed it in a vat of some kind of life sustaining fluid. Electrodes have been connected to your brain, and these are connected to a computer that generates images and sensations. Since all your information about the world is filtered through the brain, this computer would have the ability to simulate your everyday experience. If this were indeed possible, how could you ever truly prove that the world around you was real, and not just a simulation generated by a computer?

What it Means:

If you’re thinking this all sounds a bit like The Matrix, you’re right. That film, along with several other sci-fi stories and movies, was heavily influenced by the brain in a vat thought experiment. At its heart, the exercise asks you to question the nature of experience, and to consider what it really means to be human. The idea for the experiment, which was popularized by Hilary Putnam, dates all the way back to the 17th century philosopher Rene Descartes. In his Meditations on the First Philosophy, Descartes questioned whether he could ever truly prove that all his sensations were really his own, and not just an illusion caused by an “evil daemon.” Descartes accounted for this problem with his classic maxim “cogito ergo sum” (“I think therefore I am”). Unfortunately, the brain in a vat experiment complicates this argument, too, since a brain connected to electrodes could still think. The brain in a vat experiment has been widely discussed among philosophers, and many objections have been raised over its premise, but there is still no good rebuttal to its central question: how do you ever truly know what is real?